Uncertainty and inside information

Baltas, Ioannis; Yannacopoulos, A. N.

doi:10.3934/jdg.2016001

Cited by 16 publications

(5 citation statements)

References 26 publications

(54 reference statements)

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“…That is, the less the faith in the model, the more risk averse the risk manager is. This result coincides with a similar result of Baltas and Yannacopoulos [5] and Maenhout [25], who however adopt a robust control setting in different frameworks than the one studied in the present paper.…”

Section: Remark 3 Proposition 42 Is Designed For Constant Preferencsupporting

confidence: 92%

“…Therefore, in view of Equations (1), (2), (3) and (5), it follows that the wealth of the financial firm, evolves according to the stochastic differential equation…”

Section: Stochastic Differential Equation Of the Firm's Wealthmentioning

confidence: 99%

“…This method has been heavily used in the relative literature with success by many authors and within a wide range of applications, see e.g. Baltas and Yannacopoulos [5], Branger et.al [8], Cairns [14], Cont [15], Flor and Larsen [18], Korn [22], Rieder and Wopperer [34], Zawisza [40,41] and references therein.…”

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confidence: 99%

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Robust portfolio decisions for financial institutions

Baltas¹,

Xepapadeas²,

Yannacopoulos³

2018

Journal of Dynamics &Amp; Games

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The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (i) logarithmic; (ii) exponential and (iii) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

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Section: Remark 3 Proposition 42 Is Designed For Constant Preferencsupporting

confidence: 92%

“…Therefore, in view of Equations (1), (2), (3) and (5), it follows that the wealth of the financial firm, evolves according to the stochastic differential equation…”

Section: Stochastic Differential Equation Of the Firm's Wealthmentioning

confidence: 99%

See 1 more Smart Citation

Robust portfolio decisions for financial institutions

Baltas¹,

Xepapadeas²,

Yannacopoulos³

2018

Journal of Dynamics &Amp; Games

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“…That is, we need to study how build model to measure and control uncertainty. For example, some papers develop a robust-entropic optimal control technique to characterize uncertainty of model (see [2,3]). Savku adn Weber [31] use a delayed Markov regime switching jump-diffusion approach to model a stochastic optimal control problem.…”

Section: Supply Chain Coordinationmentioning

confidence: 99%

Coordinating a supply chain with demand information updating

Yang¹,

Peng²

2022

JIMO

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<p style='text-indent:20px;'>We investigate how to coordinate a two-echelon supply chain in which a supplier builds production capacity in advance and a manufacturer makes the ordering decision based on updated demand information. By combining European call option and buyback mechanisms, we propose a new hybrid option-buyback contract to coordinate such a supply chain with demand information updating. We construct a two-stage optimization model in that the supplier offers option price and the manufacturer decides initial ordering quantity in the first stage, then the supplier offers exercise price and buyback price and the manufacturer decides final ordering quantity in the second stage after demand information is updated. In both the centralized and decentralized settings, we analytically derive the optimal equilibrium solutions of two-stage ordering quantity. Particularly, we obtain closed-form formulae to describe the members' optimal behavior with a bivariate uniformly distribution. We prove that the proposed contracts can realize the perfect coordination of the supply chain and analyze how the proposed contracts affect the members' decisions. The theoretical results show that, by tuning the option price or buyback price, the supply chain profit can be arbitrarily split between the members, which is a desired property for supply chain coordination. Compared with the standard option and buyback contract, the proposed contract results in a greater supply chain profit and achieves Pareto improvement for the supply chain members. Furthermore, extending the baseline model focusing on price-independent demand to the case of price-dependent demand, we show that the proposed contract still can achieve supply chain coordination. Numerical examples are also conducted to complement the theoretical results.</p>

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“…HJB equations for the problems with the misspecification are specifically referred to as Hamilton‐Jacobi‐Bellman‐Isaacs (HJBI) equations. The multiplier‐robust control may not be the most general methodology to deal with model ambiguity, but it can offer effective and tractable mathematical descriptions of the system dynamics that potentially lead to interesting theoretical and mathematical results as in the literature . This formalism has been employed in research areas in finance and economy and insurance focusing on risk preferences of decision‐makers.…”

Section: Introductionmentioning

confidence: 99%

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Yoshioka

2019

Optim Control Appl Methods

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An optimization problem of controlling a dam installed in a river is analyzed based on a stochastic control formalism of a diffusion process under model ambiguity: a new mathematical approach to this issue. The diffusion process is a pathwise unique solution to a water balance equation considering the inflow, outflow, water loss in the reservoir, and direct rainfall. Finding the optimal reservoir operation policy reduces to solving a degenerate parabolic partial differential equation: a Hamilton-Jacobi-Bellman-Isaacs equation. A monotone finite difference scheme is constructed for discretization of the equation, successfully generating nonoscillatory and reasonably accurate numerical solutions. Stability analysis of the resulting water balance dynamics is finally carried out for both environmentally friendly and not friendly reservoir operations. KEYWORDS finite difference scheme, Hamilton-Jacobi-Bellman-Isaacs equation, reservoir operation, stochastic control, viscosity solution INTRODUCTIONThis paper contributes to providing a mathematical framework for modeling and control of reservoirs created in rivers.Since the problem has an engineering background, it is first presented, and then, the issues to be addressed and our contributions are explained.Many rivers have dams serving as central infrastructures to supply essential water resources for human lives. 1-3 The stored water in the reservoir created by a dam is utilized for multiple purposes, such as drinking water, irrigation, and hydropower generation. 4 Several dams are used for flood mitigation as well. 5,6 On the other hand, controlling a dam critically affects its downstream river environment because the original flow regime is altered. 7-9 Sediment transport and attached algae population dynamics in dam downstream experience significant changes because dams trap sediment and the algae growth is highly flow-dependent. 10 Dam operation is thus desired to be environmentally friendly such that its impacts on the downstream are minimized, while it should be fit-for-purpose at the same time.Management of environment and ecology in rivers has been a long-standing engineering problem, 11-13 and mathematical tools and concepts for their modeling, analysis, and control are still developing. Several researchers considered river management problems based on stochastic process models such as stochastic differential equations (SDEs) 14 that can naturally consider stochasticity involved in environmental and ecological processes. 15 Interactions between aquatic species, such as riparian vegetation and fishes, and river discharges have been described with SDEs. 16 Miyamoto and Kimura 17 analyzed seedling, growth, and mortality dynamics of riparian trees subject to stochastic flood disturbances. Vesipa et al 18 764

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Uncertainty and inside information

Cited by 16 publications

References 26 publications

Robust portfolio decisions for financial institutions

Robust portfolio decisions for financial institutions

Coordinating a supply chain with demand information updating

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

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